Given a matrix \( M\in \mathbb {R}^{n\times n} \)  and a vector \(q \in \mathbb {R}^n\) , the linear complementarity problem [1]}, denoted by LCP\((q,M)\) , is to find a pair of vectors \(w,z \in \mathbb {R}^n\)  such that
\(z\ge 0, ~~~ w=Mz+q\ge 0, ~~~ z^T w=0.\) 
